According to Your Story p. 106, when you invoke somebody else's aspect to make a declaration, you follow the same guidelines as invoking your own aspects for effect (p. 99).
You can also invoke an aspect for effect, using it to declare a fact or circumstance that would be of benefit to your character.
I would not rule that forcing another character to act is a “fact or circumstance” – dictating an action is a limitation, a kind of compel (p. 101). In Fate Core, it would be a decision-based compel.
Also, from the Fate Core Veterans’ Guide (p. 294):
You might have seen player-driven compels referred to as “invoking for effect.” We thought it was clearer to just call it a compel, no matter who initiates it.
Some more details.
Based on the nature of the aspect, “Susceptible to Suggestion,” and the forceful suggestion to “Show Yourself,” I interpret this as limiting a character's choices (YS101, a decision-based compel in Fate Core):
If your character would normally have a number of choices in a particular situation and acting in accordance with his aspect is going to make more trouble for the character and limit those choices, that's grounds to compel the aspect.
If the aspect were instead related to counterspelling, or something else that could contrive a circumstance making the player visible, I'd still call that a complication rather than invoking for effect (YS101, an event-based compel in Fate Core):
If everything would be going along normally and the aspect makes things more difficult or introduces an unexpected twist, that's grounds for a compel.
I would only rule it as invoking for effect if the declaration is simply adding to the story without significantly complicating things for another player. I interpret invoking for effect as roughly equivalent to declaring a story detail in Fate Core (FC13):
For example, you might use this to narrate a convenient coincidence, like . . . showing up at a dramatically appropriate moment. . . . To do this, you'll spend a fate point. You should try to justify your story details by relating them to your aspects.
This is substantially similar to the example given on YS99 of arriving “at exactly the right moment, invoking your character's Perfect Timing or Grand Entrance aspect.”